This paper deals with the description of a general method for calculating the residues of a linear system. Considering, physical models, it is well-assumed that the system described only presents simple eigenvalues, or at least simple-complex eigenvalues. However, as demonstrated in this paper, it is not completely true for all the real systems, and a method to evaluate the residues for these cases is required. In this paper, a methodology for computing the residues, even with the existence of multiple eigenvalues (described by their Jordan normal form) is developed and presented. Moreover, the calculation of the residues is applied to analyze the output-controllability of dynamic systems. Finally, some real examples are presented to validate the methodologies proposed